# Accuracy standards for sea level rise mapping

Over the last year we’ve been working on mapping the possible inundation that sea level rise would bring to the coastal community. We quickly ran into a serious question. What amount of rise can we map given the accuracy of the elevation? This ought to be an easy question. Surely there are mapping standards we could follow. Alas, there are multiple mapping standards and what you pick depends on what you think you’re doing and the assumptions you make about that process. I’m going to look at a few options for looking at the problem and maybe a different way to think about mapping standards. For my examples, I’m going to look at a case where the vertical error is about 30 cm at the 95% confidence level. That number is based upon having lidar with around 10 cm RMSE, a tidal datum transform using VDatum with an error around 11 cm RMSE, assuming independent normally distributed errors, and rounding to a nice roundish number.

If I were to consider mapping several potential sea level rise values with some interval between them, such as every two feet, that could be equivalent to mapping contours and the NMAS standards of 1947 would be applied to determine the minimum contour interval allowed. Incorporating the NSSDA standards, this would provide an allowed contour interval equal to 1.67 times the 95% confidence level. For a 95% confidence of 30 cm (combined lidar error and VDatum error), this is a contour interval of 50.1 cm or about 1.6 feet.

The federal NMAS standards aren’t the only choices for contours though. I could assume the ASPRS contour interval guidelines are more appropriate and assume class 3 (associated with large area cadastral or city planning) is the appropriate type. In this case, 30 cm accuracy at 95% confidence is sufficient for half foot contour intervals. You can find further information on the NMAS, ASPRS, and NSSDA standards on the ASPRS June 2008 Mapping Matters column.
I could look at this in a very different way. Instead of a set of contours, I could consider each sea level rise amount as an independent line that is equivalent to a single line feature such as the shoreline on a chart. The question is no longer “what’s the smallest rise I can map”, but “can I map at all”. For single line features, the NMAS standards of 1947 could be applied to determine the maximum map scale allowed. For map scales larger than 1:20,000, not more than 10 percent of the points tested shall be in error by more than 1/30 inch. Assuming our vertical 95% confidence level of 30 cm and a slope of 1 degree, the minimum scale (most zoomed in) is about 1:24,000. For a slope of 11 degrees, a map scale of 1:3,600 would be acceptable. A fine sand beach might have a 1 degree slope while a beach composed of granules might have about an 11 degree slope (http://www4.ncsu.edu/eos/users/c/ceknowle/public/chapter12/part2.html).

Finally, I could assume this is so much like doing a shoreline that you should apply the IHO standards for charting shoreline. For a natural coastline, this is either 10 m or 20 m at 95% confidence depending on chart survey type. The 10 m value is primarily for harbor areas, so the 20 m value is usually going to be more applicable. On a 1 degree slope beach, a 30 cm error equates about 17 meters horizontal error. This would be 1.5 meters on an 11 degree slope.
There might be some other ways to think about it and some other standards too. I’d certainly be glad to hear about them. While I mostly favor thinking about it as mapping potential shoreline, I also think we may be missing the goal of having map accuracy standards. In my opinion, the point of the standards is to provide the map user a sense of the positional uncertainty of features on the map or a sense of the confidence they should have. Perhaps we would be better served if we could visually show that uncertainty on the map itself. For a paper map, that is difficult to do. However, digital maps with layers that can be toggled on and off give other opportunities. We’ve headed in that direction by adding an uncertainty layer for sea level rise based upon the uncertainty of the elevation data. If you’d care to check out what we’ve done, you can see it at coast.noaa.gov/slr. That site shows an area where the wet/dry line might be instead of just the best estimate line. In this case, there is an 80% chance the blue area is wet, an 80% chance the unshaded area is dry and a 60% chance the wet/dry line is in the orange area. The confidence to use when drawing the area is certainly a topic for discussion and I look forward to hearing what people think.